OFFSET
1,1
MATHEMATICA
EngelExp[A_, n_]:=Join[Array[1&, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[ #[[1]]#[[2]]-1]], Expand[ #[[1]]#[[2]]-1]}&, {Ceiling[1/(A-Floor[A])], A-Floor[A]}, n-1]]; EngelExp[N[Sin[2], 7!], 30] (* Georg Fischer, Nov 20 2020 *)
PROG
(PARI): r=sin(2); for(i=1, 20, s=r*ceil(1/r)-1; print1(ceil(1/r), ", "); r=s); /* Benoit Cloitre [amended by Georg Fischer, Nov 20 2020] */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Mar 03 2002
EXTENSIONS
a(1)=2 inserted and a(29),a(30) from Georg Fischer, Nov 20 2020
STATUS
approved